Question

Which of the following is a point you can generate to create the parabola for the quadratic equation y = - 6x ^ 2 + 3x + 8 ? (1 point) (- 3, 323); (- 6, 8); (- 6, 206); (- 3, - 55)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find a point on the parabola generated by the quadratic equation y = -6x^2 + 3x + 8, we can substitute a value for x into the equation to solve for y. Let's try each point and see which one satisfies the equation:

Point (-3, 323):
y = -6(-3)^2 + 3(-3) + 8
y = -6(9) - 9 + 8
y = -54 - 9 + 8
y = -55
This point does not satisfy the equation.

Point (-6, 8):
y = -6(-6)^2 + 3(-6) + 8
y = -6(36) - 18 + 8
y = -216 - 18 + 8
y = -226
This point does not satisfy the equation.

Point (-6, 206):
y = -6(-6)^2 + 3(-6) + 8
y = -6(36) - 18 + 8
y = -216 - 18 + 8
y = -226
This point does not satisfy the equation.

Point (-3, -55):
y = -6(-3)^2 + 3(-3) + 8
y = -6(9) - 9 + 8
y = -54 - 9 + 8
y = -55
This point satisfies the equation.

Therefore, the correct answer is (-3, -55).

Answer 2

Given the table of values, complete the table for the quadratic equation y = - 6x ^ 2 + 3x + 8 to find the values of the high or low point of the parabola. y -1 -0.75 2.375 -0.5 5 -0.25 8 0.25 8.375 0.5 0.75 15 Which of the following is correct?

(- 1, - 1) is the low point on the parabola . (0.25, 8.375) is the low point on the parabola. (0.25, 8.375) is the high point on the parabola (0.5, 9) is the high point on the parabola.

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the high or low point of the parabola generated by the quadratic equation y = -6x^2 + 3x + 8, we need to find the vertex of the parabola. The vertex of a quadratic equation in the form y = ax^2 + bx + c is given by the coordinates (h, k), where h = -b/2a and k = f(h). In this equation, a = -6, b = 3, and c = 8.

Using the formula h = -b/2a, we can find the x-coordinate of the vertex:
h = -3/(2*(-6)) = 3/12 = 0.25

Now, to find the y-coordinate of the vertex, we substitute the value of h = 0.25 into the equation:
k = -6(0.25)^2 + 3(0.25) + 8
k = -6(0.0625) + 0.75 + 8
k = -0.375 + 8.75
k = 8.375

The vertex of the parabola is (0.25, 8.375).

Comparing the given options:
(-1, -1) is not the low point on the parabola.
(0.25, 8.375) is the correct answer. It is the low point on the parabola.
(0.25, 8.375) is not the high point on the parabola.
(0.5, 9) is not the high point on the parabola.

Therefore, the correct statement is:
(0.25, 8.375) is the low point on the parabola.

Answer 4

3- 2- 1 -0- -4 -3 -2 -1 0 1 2 2 3 3456 -1- 2 -3- -4 -5- --6- -8- the ( ) the graph (1poin) \{0, 2\}; x = 1.5; (4, 0); (0, - 4)

Answer 5

[AI-generated answer — Bot GPT 3.5]

Based on the given list of values, we can identify the points in the graph:

(3, -2)
(1, 0)
(-4, -3)
(-2, -1)
(0, -4)
(-3, -5)
(-6, -8)

Out of the given options, the point (0, -4) matches one of the points identified in the list. Therefore, the correct answer is:

(0, -4) is on the graph.

Answer 6

3- 2 -14-13-12-11-10 -7 -6 -5 -4 -3 -2 -1 0 1 -2- graph ) (- 10, 0); (- 11, - 1); x = - 11; (- 12, 0)

Answer 7

[AI-generated answer — Bot GPT 3.5]

Based on the given list of values, we can identify the points on the graph:

(3, -2)
(-14, -13)
(-12, -11)
(-10, -7)
(-6, -5)
(-4, -3)
(-2, -1)
(0, 0)
(1, -2)
(-11, -1)

Out of the given options, the point (-12, 0) is not found in the list of values. Therefore, it is not on the graph.

The other three options all match points that are found in the list of values. Therefore, the correct answer is:

(-10, 0) and (-11, -1) are on the graph. x = -11 is also on the graph.

Answer 8

6 4- 3 - 2 1 -14 -13 -12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -2- identify the vortex on the graph ) (- 10,0); (- 11, - 1); x = - 11; (- 12, 0)

Answer 9

[AI-generated answer — Bot GPT 3.5]

To identify the vertex of the graph, we need to find the highest or lowest point on the graph. The vertex of a parabola represents this highest or lowest point.

Based on the given list of values, we can identify the points on the graph:

(6, 4)
(-3, -2)
(1, -14)
(-13, -12)
(-11, -10)
(-9, -8)
(-7, -6)
(-5, -4)
(-3, -2)
(-1, 0)
(-2, -1)
(0, 0)
(1, -2)
(-11, -10)

Out of the given options, the point (-10, 0) is found on the graph. However, it is not the highest or lowest point on the graph.

To find the vertex, we need to look for the highest or lowest y-coordinate among the listed points. In this case, the point (-1, 0) has the lowest y-coordinate of 0, which means it is the lowest point on the graph. Therefore, the point (-1, 0) represents the vertex of the graph.

Among the given options, (-1, 0) is not one of the provided choices. Therefore, none of the given options correctly identify the vertex of the graph.

Answer 10

6 -3- 2- 1- 1 -0- -14-13 -12 -11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 --2- Identify the vertex on the graph point ) (- 10, 0); (- 11, - 1); x = - 11; (- 12, 0)

Answer 11

[AI-generated answer — Bot GPT 3.5]

Based on the given list of values, we can identify the points on the graph:

(6, -3)
(2, -1)
(1, 0)
(-14, 13)
(-12, 11)
(-10, 9)
(-8, 7)
(-6, 5)
(-4, 3)
(-2, 1)
(0, -1)
(-2, -1)

Out of the given options, none of them match any of the points identified in the list. Therefore, none of the given options correctly identify the vertex of the graph.